Basically, lamp units are composed of a reflecting mirror (hereinafter called “the main mirror” to distinguish it from an auxiliary reflecting mirror that will be described later) having a concave reflecting surface for reflecting light emitted from the high-pressure discharge lamp (hereinafter called “the lamp”) to the object to be irradiated. In addition, some lamp units are composed of an auxiliary reflecting mirror for reflecting light from the lamp emitted in the opposite direction of the main reflecting mirror toward the light emission center (i.e. the center between a pair of electrodes).
The auxiliary reflecting mirror improves the efficiency for utilization of the light from the lamp emitted in the opposite direction of the main reflecting mirror. As a result, it improves the light collection efficiency.
Generally, the reflecting surface of the auxiliary reflecting mirror is spherical. The surface of the auxiliary reflecting mirror is attached to the lamp such that the light emission center of the lamp is at the spherical center. Ideally, this structure allows the light from the light emission center of the light to be reflected by the reflecting surface of the auxiliary reflecting mirror, and to travel toward the surface of the main reflecting mirror after passing through the light emission center of the light. In reality, however, refraction occurs when the light from the light emission center enters the bulb of the lamp, when the light goes out of the bulb, and so on. As a result, the light emitted from the lamp towards the auxiliary reflecting mirror and reflected by the auxiliary reflecting mirror may reach the electrodes without passing between the pair of the electrodes. Thus, it can hardly be said that the light from the lamp is used effectively.
Meanwhile, there is a technique to make a correction to the reflecting surface in view of the refraction (Patent Document 1). This technique is to make a correction to the reflecting surface of the main reflecting mirror such that the light from the light emission center of the lamp will be collected at the second focal point. It is possible to apply this technique to make a correction to the reflecting surface of the auxiliary reflecting mirror such that the light from the light emission center of the lamp will be reflected by the reflecting surface of the auxiliary reflecting mirror and returns to the light emission center.    Patent Document 1: Japanese Laid-open Patent Application Publication No. 2004-265702